This page gives an overview of my current and past research interests. In all of these projects, developing a mathematical model that capture the key physics is the primary aim. To gain understanding of the problem, either numerical simulation or experimental (and sometimes both) techniques are employed.
Multiscale modelling of segregation in rotating drums and chutes
In collaboration with S.Gonzalez (former PhD student), S. Luding, W den Otter, K. Windows-Yule (former PhD student, University of Birmingham, former PostDoc), D. Parker (University of Birmingham), D.R. Tunuguntla (former PostDoc), I. Denissen (former PhD student), M. van Schrojenstein Lantman (former PhD student).
Based on the experimental and theoretical understanding of granular segregation in general, we collectively developed a new model that intends to, qualitatively and quantitatively, predict segregation for bidisperse mixtures in both rotating drums and chute flows. The model constitutes the effects of, both, particle size and density and has the ability to predict several states observed in rotating drum experiments and DPM simulations.
MercuryDPM is currently being utilised to simulate very long drums and to investigate the 3D banding instability. In the future it would be used to investigate segregating in very long chute; following on from the current work on bi-disperse bulbous head formation. Also we have investigated the effect of different shaped drums.
The experimental investigation of rotating drums has thus far proved highly fruitful, producing to date two published papers with several more in preparation. The work demonstrates various manners in which the geometry of a system may be exploited to induce, direct, strengthen or suppress segregation — all highly valuable abilities for a variety of industries and scientific fields — as well as providing a deep insight into the many different physical mechanisms underlying the segregation of rotated granular systems [35,39,46].
Additionally, the RIMS setup at EPFL has been used to get a fully 3D picture of the segregation in these drums. The data-analysis is still underway and we have developed a new more accurate way of reconstructing the particle position from RIMS data. This new image analysis code is now being generalised, such that the same code can be used to analyse all the experimental data from RIMS, optical, PEPT etc. Experimental work has also been conducted exploring the fundamental nature of segregative behaviours of these systems; specifically, a series of binary and ternary systems have been studied in order to establish whether the known segregative behaviours of the former can be used to predict those of the latter. Work is also underway providing a cross-comparison of data acquired using RIMS, PEPT and relatively simple optical imaging, in order to provide both a mutual validation of the three techniques, and a deeper insight into the systems studied than is possible using any single technique in isolation. Additionally, we are now constructing a second RIMS facility at the University of Twente.
Segregation mobility feedback
In collaboration with, M. Woodhouse (former PostDoc University of Bristol), C. Johnson (former Post Doc University of Bristol, now University of Manchester), P. Kokelaar (University of Liverpool) and N. Gray (University of Manchester) and I. Denissen (former PhD student).
It is important to be able to predict the distance to which hazardous natural granular flows (e.g. snow slab avalanches, debris-flows and pyroclastic flows) might travel, as this information is vital for accurate assessment of the risks posed by such events. In the high solids fraction regions of these flows the large particles commonly segregate to the surface, where they are transported to the margins to form bouldery flow fronts. In many natural flows these bouldery margins experience a much greater frictional force, leading to frontal instabilities. These instabilities create levees that channelise the flow vastly increasing the run-out distance.
A similar effect can be observed in dry granular experiments, which use a combination of small round and large rough particles, see figure above. When this mixture is poured down an inclined plane, particle size segregation causes the large particles to accumulate near the margins. Being rougher, the large particles experience a greater friction force and this configuration (rougher material in front of smoother) can be unstable. The instability causes the uniform flow front to break up into a series of fingers.
The model for particle size-segregation developed during my PhD has been coupled to existing avalanche models through a particle concentration dependent friction law. Numerical solutions of this coupled system has been compared to both large scale experiments carried out at the USGS flume and more controlled small scale laboratory experiments.
The coupled depth-averaged model captures the accumulation of large particles at the flow front. We show this large particle accumulation at the head of the flow can lead to the break-up of the initially uniform front into a series of fingers. However, we are unable to obtain a fully grid-resolved numerical solution; the width of the fingers decreases as the grid is refined.
By considering the linear stability of a steady, fully-developed, bi-disperse granular layer it is shown that the governing equations, while not ill-posed, are linearly unstable to arbitrarily small perturbations. It should be noted similar stability characteristics are found for shallow layer fluid flows on an inclined plane, with small wavelength perturbations stabilised by the inclusion of empirical frictional drag and viscous dissipation. Furthermore, depth-averaged models for roll waves on a mono-disperse, shallow granular layer released on an inclined plane have a similar problem with high wave-number modes remaining linearly unstable. In this case the high wavenumber instability can be suppressed by the inclusion of (phenomenological) viscous dissipation. It is possible that by including similar rheological terms in our depth-averaged model the small wavelength modes can be stabilised and a well defined finger width can be predicted.
This is the first model to describe the break-up of a uniform front of granular material, and it represents a crucial step forward in obtaining a mathematical model of this process. However, the current model is not complete and remains linearly unstable to arbitrarily small wavelength perturbations. We anticipate that these small wavelength instabilities can be stabilised by including additional physical effects, and this remains an active avenue of investigation. Details of this model can be found in , see publications page for details.
A study has been undertaken experimentally, using MercuryDPM and theoretically to investigate size-segregation in moving-bed channel. This type of geometry creates a dense gravity-driven granular flow that remains stationary in the reference frame of the lab. This is achieved by moving the bed of an inclined channel upslope. This drags the bottom layers of the granular mixture upslope whilst the upper layers avalanche downslope as a result of gravity. There are two main advantages to this geometry: firstly, RIMS can be applied on a gravity driven flow, and secondly, size-segregation leads to a horizontal separation of large and small particles thereby mimicking what occurs at avalanche fronts. The large particles accumulate at the downslope end whilst small particles accumulate at the upslope end. The main reason to study this type of flow is to investigate the feedback that exists between size-segregation and the bulk flow behaviour. It is expected that the strongest component of this feedback occurs near the front of the avalanche, where a so-called breaking size-segregation wave exists. This is a complex recirculating structure that separates the large particle front and small particle tail of the flow. Indeed our findings show the existence of a feedback, where the addition of small particles to the flow increases the traction with the bed, while simultaneously increasing the bulk flow speed. Importantly these effects reach their maximum at roughly 60% to 70% small particles in the flow, which is the result of the preferential position of small particles near the bed .
Coupling of FEM-DPM
In collaboration with S. Luding, T. Weinhart, M. Post (PhD student), H. Cheng and A. Hazel (University of Manchester)
The particle-fluid coupling is incorporated using two open-source codes: MercuryDPM as the particle solver and oomph-lib as the finite element method (FEM) fluid solver. The current work focuses on under-resolved coupling, using the Anderson-Jackson formulation, with the particle volume fraction extracted from discrete particle simulation. This will then be applied to the die filling process and powder compaction to study the tableting process. In the current state of the code, 3D two-way coupled, the behaviour of a particle-fluid system can be studied for example in particle settling (see Figure).
Additionally, as part of Dr. Weinhart’s Vidi project, ViPr, this coupling is being generalised to concurrent coupling schemes: surface coupling (SC) and volume coupling (VC) have been implemented within a concurrent multi-scale modelling framework. SC is well suited for particle-machinery interaction problems where deformation, fatigue, etc. in the structure is important (see Figure).
VC is implemented with the goal to adaptively switch from a discrete particle to a continuum model (see Figure), and vice versa, depending on a trade-off between accuracy and efficiency and relevant length/time scales. The method is further developed with the help of coarse graining which allows to map particle scale data to the macro scale while conserving mass and momentum.
Vibrofluidised Granular Materials
In collaboration with N. Rivas (former PhD student), S. Luding, D. Parker (University of Birmingham), K. Windows-Yule (former PhD student, University of Birmingham, former PostDoc) and S. Rhebergen (formerly University of Oxford, now University of Waterloo).
Agitated granular systems present behaviours which are excellent examples of non-equilibrium steady states. Their study can lead to a better general understanding of non-linear dynamics of many particle systems.
Initially, we have focused on the vertically agitated narrow bed geometry , a setup that presents many interesting states and complex transitions between them. Our approach consists in the elaboration of continuum theories that capture the observed behaviours, particle simulations and positron emission particle tracking experiments (PEPT) .
However, the powerful combination of PEPT and particle simulations has been applied more generally. Including investigating the role of buoyancy-driven convection in the segregative behaviour of a three-dimensional, binary vibrofluidised granular systems ; and, the effects of system packing, density and inelasticity on convection .
Modelling of segregation in granular flows
This work was started via my PhD, under the supervision of Prof. N. Gray. Parts of it were undertaken in collaboration with M. Shearer and A. Hogg. Now in collaboration with D.R. Tunuguntla (former PhD student, former PostDoc) and M. Post (PhD student)
This work focused on developing a continuum model of granular size-segregation from a mixture-theory framework. The study will focus on dense granular chute flows where kinetic sieving is the dominant mechanism for particle-size segregation. The basic idea is: that as grains avalanche downslope, the local void ratio fluctuates and small particles fall into the gaps that open up beneath them, as they are more likely to fit into the available space than the large ones. The small particles, therefore, migrate towards the bottom of the flow and lever the large particles upwards due to force imbalances. This was termed squeeze expulsion by Savage and Lun (1988).
In frictional flows this process is so efficient that segregated layers rapidly develop, with a region of 100% large particles separated by a concentration jump from a layer of 100% fine particles below. The figure shows the flow of red, large, dense, particles and white, small, less dense, particles from a hopper containing an approximately homogeneous mixture. A region of nearly pure, large, particles is formed near the free-surface, immediately on exiting the gate of the hopper. This layer grows in thickness as the material flows down the slope, due to the downward percolation of the smaller material. As the small material percolates, squeeze expulsion forces the large particles back upwards, forming a similar growing layer of nearly pure, small particles at the bottom of the flow. This process continues until these pure regions meet and the flow is inversely graded with large material above small.
The continuum model developed is derived based on two key assumptions: firstly, as the different particles percolate past each other there is a Darcy-style drag between the different constituents (i.e., the small and large particles) and, secondly, particles falling into void spaces do not support any of the bed weight. Since the number of voids available for small particles to fall into is greater than for large particles, it follows that a higher percentage of the small particles will be falling and, hence, not supporting any of the bed load, see publication , .
This segregation theory has been developed and extended in many directions: including the addition of a passive background fluid (see publication , ), the effect of diffusive remixing, Gray and Chugunov (2006), density effect , and the generalisation to multi-component granular flows by Gray and Ancey (2011).
Additionally, a large number of analytic solutions have been derived from this model, this includes publications [1,2,3,4,5,6,7] plus many more by other authors.
Also the coarse graining methodology has been extended to mixtures and time evolving flows . This is now one of the main research tools of the project and has already been used to accurately compare and contrast different size-segregating models in the literature. Importantly we wrote all the proposed models, for the first time, in a consistent nomenclature allowing direct comparison between the models. This work is now being extended to include the effects of particle volume fraction and density .
Currently I am involved in using the discrete particle method to perform the micro-macro transition for this model, (see section of Multiscale modeling of granular chute flows); and using the model to investigate segregation in rotating drums and cylinders (see section of Multiscale modelling of drums).
Multiscale modelling of granular chute flows
In collaboration with T. Weinhart (former PostDoc, now staff member), S. Luding, O. Bokhove and D.R. Tunuguntla (former PhD student, former PostDoc).
The project investigates dry granular flows on inclined channels with local constrictions and obstacles, using discrete element models (DEM) and Discontinuous Galerkin Finite Element Models (DGFEM). The effects of poly-dispersity and non-uniform shape of the particles will be studied for both rotating and non-rotating situations. The main challenges in the modelling of these flows is understanding the effect of rotation, particle segregation and how to deal with the co-existence of rapid and slow regimes.
Granular avalanche flows are common to natural environments and industry. They occur across many orders of magnitude. Examples range from rock slides, containing upwards of 1000m3 of material; to the flow of sinter, pellets and coke into a blast furnace for iron-ore melting; down to the flow of sand in an hour-glass. The dynamics of these flows are influenced by many factors such as: poly-dispersity; variations in density; non-uniform shape; complex basal topography; surface contact properties; coexistence of static, steady and accelerating material; and, flow obstacles and constrictions.
Discrete Particle Methods (DPMs) are an extremely powerful way to investigate the effects of these and other factors. With the rapid recent improvement in computational power the full simulation of the flow in a small hour glass of millions of particles is now feasible. However, complete DPM simulations of large-scale geophysical mass flow will, probably, never be possible.
One primary goal of the present research is to simulate large scale and complex industrial flows using granular shallow-layer equations. So far we have taken the first step of using the DPM to simulate small granular flows of mono-dispersed spherical particles in steady-flow situations. The DPM simulations undertaken to date will enable the construction of the mapping between the micro-scale and macro-scale variables and functions (the Micro-Macro transition), thus enabling construction of a closed set of continuum equations. These mappings (closure relations) can then be used in continuum shallow-layer models and compared with full DPM simulations (DPMs). For certain situations, precomputed closures should work; but, in very complicated situations the pre-established relations may fail.
So far the Micro-Macro transition has been investigated for basal friction (see pubs. [13,17]), closure relations required for shallow-granular models (i.e. velocity shape factor, normal stress difference and basal frictions), see pub. , and for binary size particles segregation, see pub. . To perform the micro-macro transition for basal friction a new method of mapping micro-macro variables had to be developed that is valid near a boundary, see pub. . Finally, the Micro-Macro transition has been used to investigate a framework for a fully three dimensional description of flowing granular materials, see pub. .
When simple precomputed closures law fail, heterogeneous, multi-scale modelling (HMM) is then an alternative in which the local constitute relations are directly used in the continuum model. In HMM, continuum and micro-scale models are dynamically coupled with a two-way communication between the different models in selective regions in both space and time, thus reducing computational expense and allowing simulation of complex granular flows.
In the future the project will focus on developing a heterogeneous multiscale model, coupling macro-scale continuum with micro-scale discrete particle models, using integrated DEM and DGFEM. The coupling will be done at selective regions in space and time thus reducing computational expense and allowing simulation of the complex granular flows under study.
Molecular simulation of ionic liquids
In collaboration with R. Sitlapersad (PhD student), R. Roij (Utrecht), P. Cats (PhD student/Utrecht ) and W. den Otter.
Electrolytes are prevalent in energy harvest and storage devices, including supercapacitors, batteries (both Li/Li+ and next generation/“beyond Li” devices), fuel cells (incl. redox flow batteries), and dye-sensitised solar cells. Ionic liquids (ILs) are superior to other electrolytes due to a unique combination of material properties, including high viscosity, low vapour pressure, inflammability, low chemical reactivity, high ionic concentration, and low dielectric constant. Whilst ILs maximise energy density, this comes at the expense of a dramatic reduction in power density, making IL devices currently niche rather than mainstream. This peculiar dynamical slowdown cannot be understood with present theories, and molecular complexity and specific ion/ion and ion/substrate interactions put optimisation of devices beyond reach.
We aim to understand this peculiar behaviour, to optimise power density for all IL technologies. We will address these issues through a combination of dynamic density functional theory and both atomistic and coarse-grained molecular dynamics simulations. We will initially work with the same systems as other sub-projects but with the ions and solvent coarse-grained. Later we will undertake fully atomistic simulations on larger systems to investigate “real” electrolyte concentrations, as well as long-range correlations in complex nanopores networks. The fully atomistic simulations will make use of so-called Cloud computing.
Multiscale modelling of agglomeration
In collaboration with T. Weinhart, S. Luding, M. Post (PhD student) D.R. Tunuguntla (PostDoc), S. Arora (former PhD student), M. Y. Shaheen (PhD student).
The aim of this project is to quantitatively predict bulk processes such as agglomeration through compression and/or heating. This will require the development and calibration of new multi-scale particle models for fine powders and their application to processes in additive manufacturing, pharmaceutics, process and mechanical engineering, geotechnics, etc; selective laser sintering (SLS) and tableting are chosen as the prototype processes to which the new techniques are applied first. The resulting numerical and analytical methods will be capable of quantitative predictions for a wide range of situations, helping to understand the fundamentals of agglomeration, but also allowing to optimise processes in the future. An especially challenging and novel aspect is the process dynamics (kinetics and rate-dependence) as well as the coupling between the individual scales.
The technical aim of the project is a mesoscale model that allows (i) the inclusion of results from microscopic modelling, (ii) calibrated dynamic modelling on the mesoscale, i.e., validated by experiments, (iii) the inclusion of moisture and the interaction with the surrounding fluid in tableting processes and the temperature dynamics in SLS into the mesoscale model, and, ultimately, (iii) the quantitative prediction of macroscopic processes and model parameters by developing new constitutive rheological relations.
Formation of a 2D ‘Hele-Shaw’ beach
In collaboration with O. Bokhove, W. Zweers. D. van der Meer. B. van der Horn (former Masters student), E. Gagarina (former PhD student).
This research combines experimental, numerical and theoretical work to examine several aspects of the formation of beaches and dunes by breaking waves in a table-top `Hele-Shaw’ beach experiment, see picture above. It consists of a narrow, just over one particle diameter wide, wave tank, in which zeolite particles act as sand and a wave maker generates the breaking waves. The major challenge is to understand the fundamental physics of beach and dune formation: a complex two-way interaction between the particulate beach and the free-surface waves. Understanding the formation and erosion of beaches is becoming increasingly important as the Netherlands’ coastline becomes more vulnerable. Our quasi two-dimensional Hele-Shaw set-up allows fundamental physics to be investigated in a controlled fashion and will also shed new light on the important natural three-dimensional problem.
The key objectives proposed are: to use the Hele-Shaw beach experiments to explore beach and dune formation, and determine fluid-particle interaction laws; and, to develop novel physical and numerical continuum models, and validate these against the laboratory experiments.
Currently there are two conference proceeding [28, 11] and the two journal articles [29, 26], on this work.
In collaboration with S. Gonzalez (former PhD student) and S. Luding.
The aim of this research is to develop a event driven algorithm for the formation of clusters in a two dimensional gas: particles move freely until they collide and “stick” together irreversibly. These clusters are allowed aggregate into bigger structures in an isotropic (random) way.
So far the research has focused on a simple “toy” model that is easy to implement in an event-driven algorithm. In  we have used this model to investigate the event-driven simulations of irreversibly aggregating clusters in 2D systems of various densities. This model leads to the formation of fractal structures and the exponent of the fractional dimension was found to be a strong function of the initial packing density.
The figure above shows the dependence on the fractal dependence on the initial packing density and two example fractional structors. There are many open questions to this research and improves that could be made to the simple model of cluster formation for event driven simulations.
Bore Soliton Splash
In collaboration with O. Bokhove and W. Zweers.
Onno Bokhove was asked to make a soliton in an irrigation channel for the opening of the new university square in September 2010. He said yes, but a soliton was too boring for a large crowd; therefore the idea of making a splash at the end was developed. Very quickly the team was extended to include me and Wout Zweers and mathematical theory was put into practice.
In testing sensitivity to the initial water height was observed. With a two centimetre changing the splash from 2 metre to 4 metres in height. The high splash case also contained a bore (hence the name of this experiment) and it is the complex interaction of this bore and a soliton which generates this vertical jet.
There is current one popular science article on this experiment,  on the publications list. Also for more videos and information on this experiment, including the new mini bore-soliton splash, see website maintain by W. Zweers.
This project was started as part of the Study Group Mathematics with Industry 2010. Was continued in collaboration with O. Bokhove and D. van der Sar.
The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runoff water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity.
The aim of this work is to develop a model of algae production and use this model to investigate how best to optimise algae farms to satisfy the dual goals of maximising growth and removing mineral contaminants.
The original SWI report can be found on the publication page number .